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README.md

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### Breaking Change in Version 0.5
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> The default `Tableau(A, b, c)` creates a tableau for an LP in *standard* form. To create a tableau in *canonical* form, use `Tableau(A, b, c, true)`.
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> The default `Tableau(A, b, c)` creates a tableau for an LP in *standard* form. To create a tableau for a *canonical* LP, use `Tableau(A, b, c, true)`.
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The rationale for this change is that the Simplex Method operates on standard form LPs, so that should be the default. Hence, `Tableau(A, b, c)` is equivalent to `Tableau(A, b, c, false)`
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{"documenter":{"julia_version":"1.12.3","generation_timestamp":"2025-12-26T17:13:49","documenter_version":"1.16.1"}}
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{"documenter":{"julia_version":"1.12.3","generation_timestamp":"2026-01-03T16:54:55","documenter_version":"1.16.1"}}

docs/build/api/index.html

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docs/build/dual/index.html

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julia> c = [3, 4, 7];
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julia> T = Tableau(A,b,c):
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julia> T = Tableau(A,b,c,true)
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┌──────────┬───┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
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│ │ z │ x_1 │ x_2 │ x_3 │ x_4 │ x_5 │ x_6 │ x_7 │ x_8 │ x_9 │ RHS │
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│ Cons 1 │ 0 │ -11 │ -8 │ -8 │ -6 │ -4 │ -2 │ -1 │ 0 │ 0 │ -3 │
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│ Cons 2 │ 0 │ -2 │ -6 │ -8 │ -5 │ -1 │ 1 │ 0 │ -1 │ 0 │ -4 │
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│ Cons 3 │ 0 │ -11 │ -9 │ -5 │ -8 │ -2 │ -4 │ 0 │ 0 │ -1 │ -7 │
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└──────────┴───┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘</code></pre><p>The result of <code>simplex_solve!(dT)</code> is <span>$-15/2$</span>. </p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.16.1 on <span class="colophon-date" title="Friday 26 December 2025 17:13">Friday 26 December 2025</span>. Using Julia version 1.12.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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└──────────┴───┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘</code></pre><p>The result of <code>simplex_solve!(dT)</code> is <span>$-15/2$</span>. </p></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.16.1 on <span class="colophon-date" title="Saturday 3 January 2026 16:54">Saturday 3 January 2026</span>. Using Julia version 1.12.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

docs/build/index.html

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<!DOCTYPE html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Overview · SimplexTableaux</title><meta name="title" content="Overview · SimplexTableaux"/><meta property="og:title" content="Overview · SimplexTableaux"/><meta property="twitter:title" content="Overview · SimplexTableaux"/><meta name="description" content="Documentation for SimplexTableaux."/><meta property="og:description" content="Documentation for SimplexTableaux."/><meta property="twitter:description" content="Documentation for SimplexTableaux."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>SimplexTableaux</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Overview</a></li><li><a class="tocitem" href="tutorial/">Tutorial</a></li><li><a class="tocitem" href="other/">Other Functions</a></li><li><a class="tocitem" href="api/">API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Overview</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Overview</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/scheinerman/SimplexTableaux.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/scheinerman/SimplexTableaux.jl/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="SimplexTableaux"><a class="docs-heading-anchor" href="#SimplexTableaux">SimplexTableaux</a><a id="SimplexTableaux-1"></a><a class="docs-heading-anchor-permalink" href="#SimplexTableaux" title="Permalink"></a></h1><p>This module demonstrates how to solve linear programs using the Simplex Method.</p><p>In particular, it can be used to solve feasible optimization problems of the form <span>$\min c^T x$</span> subject to <span>$Ax ≥ b$</span> and <span>$x \ge 0$</span> (canonical form) and of the form <span>$\min c^T x$</span> subject to <span>$Ax = b$</span> and <span>$x \ge 0$</span> (standard form).</p><blockquote><p>See the <strong>Tutorial</strong> for a thorough introduction to this module.</p></blockquote><p>This is a demonstration project for illustrating the Simplex Method and for solving small linear programs. All arithmetic is exact (using arbitrary precision rational numbers).</p><p>This module serves as a supplement to the (currently under construction) textbook <a href="https://www.ams.jhu.edu/ers/books/mathematical-optimization/"><em>Mathematical Optimization: From Knowledge to Wisdom</em></a>.</p><h3 id="Feedback-please"><a class="docs-heading-anchor" href="#Feedback-please">Feedback please</a><a id="Feedback-please-1"></a><a class="docs-heading-anchor-permalink" href="#Feedback-please" title="Permalink"></a></h3><p>I am hoping this module is useful for those learning the Simplex Method. Whether you are a student or an instructor, I would appreciate <a href="mailto:ers@jhu.edu">your feedback</a>. </p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="tutorial/">Tutorial »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.16.1 on <span class="colophon-date" title="Friday 26 December 2025 17:13">Friday 26 December 2025</span>. Using Julia version 1.12.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Overview · SimplexTableaux</title><meta name="title" content="Overview · SimplexTableaux"/><meta property="og:title" content="Overview · SimplexTableaux"/><meta property="twitter:title" content="Overview · SimplexTableaux"/><meta name="description" content="Documentation for SimplexTableaux."/><meta property="og:description" content="Documentation for SimplexTableaux."/><meta property="twitter:description" content="Documentation for SimplexTableaux."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>SimplexTableaux</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Overview</a></li><li><a class="tocitem" href="tutorial/">Tutorial</a></li><li><a class="tocitem" href="other/">Other Functions</a></li><li><a class="tocitem" href="api/">API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Overview</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Overview</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/scheinerman/SimplexTableaux.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/scheinerman/SimplexTableaux.jl/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="SimplexTableaux"><a class="docs-heading-anchor" href="#SimplexTableaux">SimplexTableaux</a><a id="SimplexTableaux-1"></a><a class="docs-heading-anchor-permalink" href="#SimplexTableaux" title="Permalink"></a></h1><p>This module demonstrates how to solve linear programs using the Simplex Method.</p><p>In particular, it can be used to solve feasible optimization problems of the form of the form <span>$\min c^T x$</span> subject to <span>$Ax = b$</span> and <span>$x \ge 0$</span> (standard form) as well as <span>$\min c^T x$</span> subject to <span>$Ax ≥ b$</span> and <span>$x \ge 0$</span> (canonical form)</p><blockquote><p>See the <strong>Tutorial</strong> for a thorough introduction to this module.</p></blockquote><p>This is a demonstration project for illustrating the Simplex Method and for solving small linear programs. All arithmetic is exact (using arbitrary precision rational numbers).</p><p>This module serves as a supplement to the (currently under construction) textbook <a href="https://www.ams.jhu.edu/ers/books/mathematical-optimization/"><em>Mathematical Optimization: From Knowledge to Wisdom</em></a>.</p><h3 id="Feedback-please"><a class="docs-heading-anchor" href="#Feedback-please">Feedback please</a><a id="Feedback-please-1"></a><a class="docs-heading-anchor-permalink" href="#Feedback-please" title="Permalink"></a></h3><p>I am hoping this module is useful for those learning the Simplex Method. Whether you are a student or an instructor, I would appreciate <a href="mailto:ers@jhu.edu">your feedback</a>. </p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="tutorial/">Tutorial »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.16.1 on <span class="colophon-date" title="Saturday 3 January 2026 16:54">Saturday 3 January 2026</span>. Using Julia version 1.12.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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